represents a sum of terms.
- Plus has attributes Flat, Orderless, and OneIdentity.
- The default value for arguments of Plus, as used in x_. patterns, is 0. »
- Plus is taken to be 0.
- Plus[x] is x.
- x+0 evaluates to x, but x+0.0 is left unchanged.
- In mixed fractions such as 1 , the implicit addition can be entered as 1 + or 1 \[ImplicitPlus] . This evaluates to 1+, but implicit addition is an operator with much higher precedence than +.
- Unlike other functions, Plus applies built‐in rules before user‐defined ones. As a result, it is not possible to make definitions such as 2+2=5.
Background & Context
- Plus is a function that does addition (summation) of expressions. The expression Plus[a,b,c,…] is commonly represented using the shorthand syntax a+b+c+…. Special cases include Plus, which is taken to be 0, and Plus[x], which is taken to be x.
- Plus sorts its arguments and collapses any terms of the same type. Plus also threads element-wise over lists.
- To perform summation at a particular level of a list or to apply compensative summation to reduce numerical error for inexact summands, the function Total can be used. Accumulate gives a list of the successive accumulated totals of elements in a list. AddTo, Increment, and PreIncrement can be used to increase the value of a given variable. Minus gives the arithmetic negation of an expression, and Subtract gives the difference of two numbers.
- Summation of a function over a range or list of arguments is done using the function Sum.
Examplesopen allclose all
Plus threads element-wise over lists:
Properties & Relations (10)
Plus sorts its arguments:
Display the FullForm of a sum:
Pattern matching works with Plus:
Distribute a function over Plus:
Distribute Plus through a head:
Accumulate makes a cumulative sum: